Real-Time Feynman Path Integral Realization of Instantons

TL;DR

This paper demonstrates how quantum tunneling amplitudes, traditionally associated with Euclidean instantons, can be represented within real-time Feynman path integrals using advanced mathematical frameworks.

Contribution

It introduces a novel method to encode tunneling amplitudes in real-time path integrals by applying Picard-Lefschetz and resurgence theories, bridging a gap in quantum mechanics.

Findings

Real-time path integrals can encode tunneling phenomena.

Picard-Lefschetz theory aids in analyzing complex path integrals.

Resurgence theory connects different quantum regimes.

Abstract

In Euclidean path integrals, quantum mechanical tunneling amplitudes are associated with instanton configurations. We explain how tunneling amplitudes are encoded in real-time Feynman path integrals. The essential steps are borrowed from Picard-Lefschetz theory and resurgence theory.